calculate all polynomial for which
If we presume that p(x) is going to have at least real coefficients we can expland the definig equation to get
The above says that p(x) must contain a factor of x + 1 and since no real p(0) exists (ala Opalg) we must also require that p(x) contains a factor of x as well, so we have
where q(x) is a polynomial. This expression needs to be run through the original equation to get restrictions on q(x), but I can't make any sense out of the resulting equation.
-Dan